Chapter 4.6, Problem 32MS

Cubical spheres (ExH). Take a cube. Put a point in the middle of each face. Now draw the straight lines to the middles of each of the sides of that facc, thus producing a plus $(+)$ sign on each face. The kinked line that goes from the center of one face to the center of an adjacent face forms a bent edge on this cubical world. Thus we have created eight “bent” triangles whose vertices are the centers of the faces of the cube. Now what is the sum of the angles for each of those triangles? What is the sum of all the angles of all the triangles? Compare your answer to the answer to Mindscapc 27.